<p>The design of cryptographic hash functions is crucial for ensuring the security of digital information. In this context, cellular automata (CAs) have emerged as a promising tool due to their inherent parallelism, determinism, and simplicity. However, traditional CAs may not fully meet the requirements for cryptographic hash functions in terms of randomness, collision resistance, and avalanche effect. To address these challenges, we propose a design of cryptographic hash functions based on improved cellular automata. Our approach involves refining the rules of CAs to enhance their cryptographic properties. By incorporating random chaotic rules and optimizing parameters, we create a hash function that exhibits excellent performance in terms of randomness, collision resistance, and avalanche effect. Furthermore, the parallel nature of CAs allows for the simultaneous processing of multiple data blocks, significantly improving the efficiency of the hash function. Our design leverages these advantages to provide a robust and efficient cryptographic hash function that is suitable for a wide range of applications.</p>